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Diffstat (limited to 'Master/texmf-dist/tex')
| -rw-r--r-- | Master/texmf-dist/tex/generic/realcalc/realcalc.tex | 581 |
1 files changed, 0 insertions, 581 deletions
diff --git a/Master/texmf-dist/tex/generic/realcalc/realcalc.tex b/Master/texmf-dist/tex/generic/realcalc/realcalc.tex deleted file mode 100644 index be46167fc41..00000000000 --- a/Master/texmf-dist/tex/generic/realcalc/realcalc.tex +++ /dev/null @@ -1,581 +0,0 @@ -%% realcalc.tex -%% -%% (C) Frank Buchholz, Jan. 1993 -%% e-mail: buchholz@lusty.informatik.uni-dortmund.de -% User documentation: All lines starting with two % -% Try grep to extract these lines. -%% -%% Real arithmetic with big values and high precision. -%% Calculations are done with 9 decimal digits. -%% Usable with TeX and LaTeX. -%% -%% Parameter: -%% -%% <macro> Macro, witch catches the result. -%% <value> String or macro witch expands to a value in the range -%% from -2147483647.999999999 to 2147483647.999999999 -%% <precision> Number from 0 to 9 -%% -%% Functions: -%% - -% Don't read this file twice -\ifx\Radd\undefined \else \endinput \fi - -% Make "@" be a letters -\chardef\catamp=\the\catcode`\@ -\catcode`@=11 - -\def\@Rversion{Version 1.0, Jan. 1993} -\message{`Real arithmetic', \@Rversion (C) Frank Buchholz} - -% Allocation of temporary registers -\newcount\@ta -\newcount\@tb -% -\newcount\@xs % Sign of 1st value -\newcount\@xi % Integer part of 1st value -\newcount\@xf % Fractional part of 1st value -% -\newcount\@ys % Sign of 2nd value -\newcount\@yi % Integer part of 2nd value -\newcount\@yf % Fractional part of 2nd value -% -\newcount\@mil \@mil=1000000000 % 10^9 -% -\countdef\@xa240 -\countdef\@xb241 -\countdef\@xc242 -\countdef\@xd243 -\countdef\@xe244 -\countdef\@ya245 -\countdef\@yb246 -\countdef\@yc247 -\countdef\@yd248 -\countdef\@ye249 -\let\@f=\@tb -\let\@product=\@ta - -\chardef\@zero=0 - -%% \Radd<macro><value><value> Addition -\def\Radd#1#2#3{\@callc\@Radd#1{#2}{#3}} - -%% \Rsub<macro><value><value> Subtraction -\def\Rsub#1#2#3{\@callc\@Radd#1{#2}{-#3}} - -\def\@Radd#1#2.#3.#4\relax#5.#6.#7\relax{% - % #1 Macro, witch gets the result - % #2 integer part of 1st value - % #3 fractional part of 1st value - % #4 dummy to swallow everthing after the 2nd '.' - % #5 integer part of 2nd value - % #6 fractional part of 2nd value - % #7 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#2}{#3}% - \@readvalue\@ys\@yi\@yf{#5}{#6}% - % - % Add integer parts - \@ta=\@xi \advance\@ta\@yi% - % - % Add fractional parts if they are not zero - \ifnum\@xf=\@zero% - \ifnum\@yf=\@zero% - \@tb=\@zero% - \else% - \@longadd% - \fi% - \else% - \@longadd% - \fi% - % - % Store result - \@store#1\@ta\@tb% -} - -\def\@longadd{% - % Propagate sign to fractional parts - \multiply\@xf\@xs \multiply\@yf\@ys% - % - % Add fractional parts - \@tb=\@xf \advance\@tb\@yf% - % - % Calculate carry - \ifnum\@tb<\@zero% - \ifnum\@tb<-\@mil \advance\@ta -\@ne \advance\@tb\@mil \fi% - \else% - \ifnum\@tb<\@mil \else \advance\@ta \@ne \advance\@tb-\@mil \fi% - \fi% -} - -%% \Rmul<macro><value><value> Multiplication -\def\Rmul#1#2#3{\@callc\@Rmul#1{#2}{#3}} - -\def\@Rmul#1#2.#3.#4\relax#5.#6.#7\relax{% - % #1 Macro, witch gets the result - % #2 integer part of 1st value - % #3 fractional part of 1st value - % #4 dummy to swallow everthing after the 2nd '.' - % #5 integer part of 2nd value - % #6 fractional part of 2nd value - % #7 dummy to swallow everthing after the 2nd '.' - % - % How to do real multiplications: - % Split values in various parts - % x y = 1234 567890 . 123 456 789 - % -> xa xb xc xd xe - % -> ya yb yc yd ye - % Do 21 (!) integer multiplications if there are any fractional parts - % r = x * Y - % -> r = xi*yi - % + (xa*yc + xa*yc )*10^3 - % + (xa*yd + xd*ya )*10^-0 - % + (xa*ye + xe*ya + xb*yc + xc*yb)*10^-3 - % + (xb*yd + xd*yb + xc*yc )*10^-6 - % + (xb*ye + xe*yb + xc*yd + xd*yc)*10^-9 - % + (xc*ye + xe*yc + xd*yd )*10^-12 - % + (xd*ye + xe*yd )*10^-15 - % + (xe*ye )*10^-18 - % - % -> r = ((((( xe*ye / 1000 - % + xd*ye + xe*yd ) / 1000 - % + xc*ye + xe*yc + xd*yd ) / 1000 - % + xb*ye + xe*yb + xc*yd + xd*yc ) / 1000 - % + xb*yd + xd*yb + xc*yc ) / 1000 - % + xa*ye + ye*xa + xb*yc + xc*yb ) / 1000 - % + xa*yd + xd*ya + (xa*yc + ya*xc)*1000 + xi*yi - % The last three digigs are saved just before the divisions. - % - % Init - % - \@readvalue\@xs\@xi\@xf{#2}{#3}% - \@readvalue\@ys\@yi\@yf{#5}{#6}% - % - % Sign - \multiply\@xi\@xs% - \multiply\@yi\@ys% - \multiply\@xs\@ys% - % - \@product=\@zero% - % - \ifnum\@xf=\@zero% - \ifnum\@yf=\@zero% - % No fractional parts - \edef\@frac{000000000} % digits of fractional part - \else% - \@longmul % Long multiplication - \fi% - \else% - \@longmul % Long multiplication - \fi% - % - % Multiply integer parts - \count@=\@xi \multiply\count@\@yi% - \advance\@product\count@% - % - % Sign - \multiply\@product\@xs% - % - % Store result - \edef#1{\number\@product.\@frac}% -} - -% Do long multiplication -\def\@longmul{% - % Split values in pieces - \@f=1000000% - \count@=\@xi% - \divide\count@\@f \@xa=\count@% - \multiply\count@-\@f \advance\count@\@xi \@xb=\count@% - \count@=\@xf% - \divide\count@\@f \@xc=\count@% - \multiply\count@-\@f \advance\count@\@xf% - \@f=1000% - \@xe=\count@% - \divide\count@\@f \@xd=\count@% - \multiply\count@-\@f \advance\count@\@xe \@xe=\count@% - % - \@f=1000000% - \count@=\@yi% - \divide\count@\@f \@ya=\count@% - \multiply\count@-\@f \advance\count@\@yi \@yb=\count@% - \count@=\@yf% - \divide\count@\@f \@yc=\count@% - \multiply\count@-\@f \advance\count@\@yf% - \@f=1000% - \@ye=\count@% - \divide\count@\@f \@yd=\count@% - \multiply\count@-\@f \advance\count@\@ye \@ye=\count@% - % - \edef\@frac{} % digits of fractional part - % - \@mul ee \relax\@shift % 10^-18 - \@mul de ed \relax\@shift % 10^-15 - \@mul ce ec dd \relax\@shift % 10^-12 - \@mul be eb cd dc \relax\@saveshift % 10^-9 - \@mul bd db cc \relax\@saveshift % 10^-6 - \@mul ae ea bc cb \relax\@saveshift % 10^-3 - \multiply\@xa\@f \multiply\@xc\@f % 10^3 - \@mul ad da ac ca \relax% -} - -\def\@mul#1#2#3{% - \count@=\csname @x#1\endcsname% - \multiply\count@\csname @y#2\endcsname% - \advance\@product\count@% - % - \ifx#3\relax% - \let\next=\relax% - \else% - \let\next=\@mul% - \fi% - \next#3% -} - -\def\@shift{% - \divide\@product\@f% -} - -\def\@saveshift{% - % Save rightmost digits - \count@=\@product% - \divide\@product\@f% - \multiply\@product\@f% - \advance\count@-\@product% - \advance\count@\@f% - \edef\@frac{\expandafter\@ignorenext\number\count@\@frac}% - % - \divide\@product\@f% -} - -%% \Rdiv<macro><value><value> Division -\def\Rdiv#1#2#3{\@callc\@Radd#1{#2}{#3}} - -\def\@Rdiv#1#2.#3.#4\relax#5.#6.#7\relax{% - % #1 Macro, witch gets the result - % #2 integer part of 1st value - % #3 fractional part of 1st value - % #4 dummy to swallow everthing after the 2nd '.' - % #5 integer part of 2nd value - % #6 fractional part of 2nd value - % #7 dummy to swallow everthing after the 2nd '.' - % - \message{Error: Rdiv not ready} - % - \@readvalue\@xs\@xi\@xf{#2}{#3}% - \@readvalue\@ys\@yi\@yf{#5}{#6}% - % - \ifnum\@yi=\@zero - \@xi=\@zero - \else - \divide\@xi\@yi - \fi - % - \@store#1\@xi\@xf% -} - -%% \Rneg<macro><value> Negation -\def\Rneg#1#2{% - % Expand the value and split it into the integer and the fractional part - \edef\next{\noexpand\@Rneg\noexpand#1#2..\noexpand\relax}% - \next% -} - -\def\@Rneg#1#2.#3.#4\relax{ - % #1 Macro, witch gets the result - % #2 Integer part of value - % #3 Fractional part of value - % #4 Remaining tokens - % - \@readvalue\@xs\@xi\@xf{#2}{#3}% - % - % Change sign - \multiply\@xi-\@ne% - \multiply\@xf-\@xs% - % - % Store result - \@store#1\@xi\@xf% -} - -%% -%% \Rtrunc<macro><precision><value> Truncate value to specified precision -\def\Rtrunc#1#2#3{% - % Expand parameter and split the value into the integer and fractional part - \edef\next{\noexpand\@Rtrunc\noexpand#1#2#3..\noexpand\relax}% - \next% -} - -\def\@Rtrunc#1#2#3.#4.#5\relax{% - % #1 Macro, witch gets the result - % #2 Number of decimal places - % #3 Integer part of value - % #4 Fractional part of value - % #5 dummy to swallow everthing after the 2nd '.' - % - \count@=#2% - \edef\next{\empty}% - \ifnum\count@>\@zero% - \expandafter\@@Rtrunc#4000000000\relax% - \fi% - \edef#1{#3\next}% -} - -\def\@@Rtrunc#1#2#3#4#5#6#7#8#9{% - % #1...#9 fractional part, padded with trailing zeros - \edef\next{.#1% - \ifnum\count@>1 #2\fi% - \ifnum\count@>2 #3\fi% - \ifnum\count@>3 #4\fi% - \ifnum\count@>4 #5\fi% - \ifnum\count@>5 #6\fi% - \ifnum\count@>6 #7\fi% - \ifnum\count@>7 #8\fi% - \ifnum\count@>8 #9\fi% - }% - \@swallow% -} - -%% -%% \Rifle<value><value> Test v1 < v2 -\def\Rifle#1#2{\@callb\@Rifle{#1}{#2}} - -\def\@Rifle#1.#2.#3\relax#4.#5.#6\relax{% - % #1 integer part of 1st value - % #2 fractional part of 1st value - % #3 dummy to swallow everthing after the 2nd '.' - % #4 integer part of 2nd value - % #5 fractional part of 2nd value - % #6 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - \@readvalue\@ys\@yi\@yf{#4}{#5}% - % - \ifnum\@xs<\@ys% - \Rtesttrue% - \else% - \ifnum\@xs>\@ys% - \Rtestfalse% - \else% - \Rtestfalse% - \ifnum\@xi<\@yi \Rtesttrue \fi% - \ifnum\@xi=\@yi% - \multiply\@xf\@xs \multiply\@yf\@ys% - \ifnum\@xf<\@yf \Rtesttrue \fi% - \fi% - \fi% - \fi% - % - \ifRtest% -} - -%% \Rifeq<value><value> Test v1 = v2 -\def\Rifeq#1#2{\@callb\@Rifeq{#1}{#2}} - -\def\@Rifeq#1.#2.#3\relax#4.#5.#6\relax{% - % #1 integer part of 1st value - % #2 fractional part of 1st value - % #3 dummy to swallow everthing after the 2nd '.' - % #4 integer part of 2nd value - % #5 fractional part of 2nd value - % #6 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - \@readvalue\@ys\@yi\@yf{#4}{#5}% - % - \Rtestfalse% - \ifnum\@xi=\@yi\ifnum\@xf=\@yf \Rtesttrue \fi\fi% - \ifRtest% -} - -%% \Rifgt<value><value> Test v1 > v2 -\def\Rifgt#1#2{\@callb\@Rifgt{#1}{#2}} - -\def\@Rifgt#1.#2.#3\relax#4.#5.#6\relax{% - % #1 integer part of 1st value - % #2 fractional part of 1st value - % #3 dummy to swallow everthing after the 2nd '.' - % #4 integer part of 2nd value - % #5 fractional part of 2nd value - % #6 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - \@readvalue\@ys\@yi\@yf{#4}{#5}% - % - \ifnum\@xs>\@ys% - \Rtesttrue% - \else% - \ifnum\@xs<\@ys% - \Rtestfalse% - \else% - \Rtestfalse% - \ifnum\@xi>\@yi \Rtesttrue \fi% - \ifnum\@xi=\@yi% - \multiply\@xf\@xs \multiply\@yf\@ys% - \ifnum\@xf>\@yf \Rtesttrue \fi% - \fi% - \fi% - \fi% - % - \ifRtest% -} - -%% \Rifneg<value> Test v < 0 -\def\Rifneg#1{\@calla\@Rifneg{#1}} - -\def\@Rifneg#1.#2.#3\relax{% - % #1 Integer part of value - % #2 Fractional part of value - % #3 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - % - \ifnum\@xs<0 \Rtesttrue \else \Rtestfalse \fi% - \ifRtest% - } - -%% \Rifzero<value> Test v = 0 -\def\Rifzero#1{\@calla\@Rifzero{#1}} - -\def\@Rifzero#1.#2.#3\relax{% - % #1 Integer part of value - % #2 Fractional part of value - % #3 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - % - \Rtestfalse% - \ifnum\@xi=\@zero \ifnum\@xf=\@zero \Rtesttrue \fi \fi% - \ifRtest% -} - -%% \Rifpos<value> Test v >= 0 -%% Take care to have a corresponding \fi -\def\Rifpos#1{\@calla\@Rifpos{#1}} - -\def\@Rifpos#1.#2.#3\relax{% - % #1 Integer part of value - % #2 Fractional part of value - % #3 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - % - \ifnum\@xs<0 \Rtestfalse \else \Rtesttrue \fi% - \ifRtest% -} - -%% \Rifint<value> Test v is an integer value -%% Take care to have a corresponding \fi -\def\Rifint#1{\@calla\@Rifint{#1}} - -\def\@Rifint#1.#2.#3\relax{% - % #1 Integer part of value - % #2 Fractional part of value - % #3 dummy to swallow everthing after the 2nd '.' - % - \@readvalue\@xs\@xi\@xf{#1}{#2}% - % - \ifnum\@xf=0 \Rtesttrue \else \Rtestfalse \fi% - \ifRtest% -} - -% Utility macros - -\def\@calla#1#2{% - % #1 Macro to call - % #2 Value - % Expand the value and split them into the integer and the fractional part - \edef\next{\noexpand#1#2..\noexpand\relax}% - \next% -} - -\def\@callb#1#2#3{% - % #1 Macro to call - % #2 1st value - % #3 2nd value - % Expand the values and split them into the integer and the fractional parts - \edef\next{\noexpand#1#2..\noexpand\relax#3..\noexpand\relax}% - \next% -} - -\def\@callc#1#2#3#4{% - % #1 Macro to call - % #2 Macro, witch gets the result - % #3 1st value - % #4 2nd value - % Expand the values and split them into the integer and the fractional parts - \edef\next{\noexpand#1\noexpand#2#3..\noexpand\relax#4..\noexpand\relax}% - \next% -} - -%% \ifRtest ... \else ... \fi Re-execute the last test -\newif\ifRtest - -% -% Read value -% -\def\@readvalue#1#2#3#4#5{% - % #1 macro to catch the sign ( -1 or 1 ) - % #2 macro to catch the integer part (maybe negative) - % #3 macro to catch the fractional part (positive) - % #4.#5 value - % - % Regular expression [-...d]d...["."[d...]] - % Attention: There has to be at least one digit between "-" and "."! - % - % Integer part - \if !#4! #2=\@zero \else #2=#4 \fi% - % - % Sign - \ifnum#2<\@zero #1=-\@ne \else #1=\@ne \fi% - \ifnum#2=\@zero \ifnum #4#5<\@zero #1=-\@ne \fi \fi% - % - % Fractional part - \if !#5!% - #3=\@zero% - \else% - \@@setcount@#5000000000\relax% - #3=\count@% - \fi% -} - -% Set count@ to fractional part with trailing zeros -\def\@@setcount@#1#2#3#4#5#6#7#8#9{% - % #1...#9 fractional part, padded with '0' - \count@=#1#2#3#4#5#6#7#8#9% - \@swallow% -} - -% Swallow everything up to next \relax -\def\@swallow#1\relax{} - -% -% Store result -% -\def\@store#1#2#3{% - % #1 marcro to catch the result - % #2 counter with integer part (maybe negative) - % #3 counter with fractional part (maybe negative} - % - % Sign - \edef#1{}% - \count@=#3% - \ifnum\count@<\@zero% - \count@=-\count@% - \ifnum#2=\@zero% - \edef#1{-}% - \fi% - \fi% - % - % Pad fractional part with leading zeros - \advance\count@\@mil% - % - % Store result - \edef#1{#1\number#2.\expandafter\@ignorenext\number\count@}% -} - -% Ignore next token -\def\@ignorenext#1{} - -% Restore catcode of "@" -\catcode`\@=\catamp |